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Thread: Arrangements question

  1. #1
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    Arrangements question

    Question:

    A boy has five blue marbles, four green marbles and three red marbles. In how many ways can be arrange four of them in a row, if the marbles of any one colour are indistinguishable?

    The if blue 1...... blue 5 are all indistinguishable this is the same for green and red




    thus the answer would be $\displaystyle \frac{12!}{5!4!3!} = 27720 $ but the answer is 80 in the book where did i go wrong?
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  2. #2
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    Re: Arrangements question

    Quote Originally Posted by bigmansouf View Post
    Question:
    A boy has five blue marbles, four green marbles and three red marbles. In how many ways can be arrange four of them in a row, if the marbles of any one colour are indistinguishable?
    The if blue 1...... blue 5 are all indistinguishable this is the same for green and red
    thus the answer would be $\displaystyle \frac{12!}{5!4!3!} = 27720 $ but the answer is 80 in the book where did i go wrong?
    You need to rewrite the question. I think that it means that just four of the marbles are in the row.
    All blue, all green, three blue & one green, three blue & one red etc.
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  3. #3
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    Re: Arrangements question

    4B 1 way

    3B 8 ways

    2B 24 ways

    1B 32 ways

    no blue 15 ways
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  4. #4
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    Re: Arrangements question

    Quote Originally Posted by Idea View Post
    4B 1 way

    3B 8 ways

    2B 24 ways

    1B 32 ways

    no blue 15 ways
    Please can you explain how you got the answer

    My way of thinking

    5 Blue 4 Green 3 Red

    All blue B B B B - 1 way

    3 blues B B B
    for the last place We can choose Green 4 times or Red 3 times, I thought the the answer will be 7 since there are 7 (4 green + 3 red) for a person to choose from
    how is it 8 ways

    2 blues B B
    for the last two places We can choose Green 4 times or Red 3 times or a combination of both

    so B B G R
    4 3 = 4 X 3 = 12 ways
    or B B G G
    4 3 = 4 X 3 = 12 ways
    or B B R R
    4 3 = 4 X 3 = 12 ways

    12 + 12 + 12 = 36 ways

    I dont understand how you arrive at each answer
    Last edited by bigmansouf; May 16th 2019 at 09:26 AM.
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  5. #5
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    Re: Arrangements question

    These are the 8 ways with 3 blue marbles

    B B B G
    B B G B
    B G B B
    G B B B

    B B B R
    B B R B
    B R B B
    R B B B


    note that the marbles of any one colour are indistinguishable
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